The difference between simple interest and compound interest on a certain sum of money at 20% per annum for 2 years is Rs. 56. What is the sum?

Introduction / Context:
This is a classic question that uses the standard formula for the difference between compound interest and simple interest for 2 years at the same rate and on the same principal. The small difference is used to back calculate the principal.

Given Data / Assumptions:

• Rate of interest r = 20% per annum.
• Time period t = 2 years.
• Difference between compound interest and simple interest = Rs. 56.
• Interest in the compound case is compounded annually.
• Principal P is the same in both cases and is to be found.

Concept / Approach:

For 2 years, simple interest is SI2 = P * r * 2 / 100. Compound interest is CI2 = P * [(1 + r / 100)^2 - 1]. The difference D = CI2 - SI2 simplifies to D = P * r^2 / 100^2. Once D and r are known, we can solve this simple equation for P directly.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

The other options produce very different differences. Substituting Rs. 3680, Rs. 2650, or Rs. 1170 into the difference formula does not yield 56. Only the principal of Rs. 1400 is consistent with the given difference at 20% per annum for 2 years.

Common Pitfalls:

Some students forget the compact difference formula and attempt long calculations of compound and simple interest separately, increasing the chance of arithmetic errors. Another common mistake is to misinterpret the given difference as a percentage rather than a monetary amount.

Final Answer:

The sum is Rs. 1400.